Read and Follow Instructions Carefully: Show all your work by steps for each pro
ID: 3315221 • Letter: R
Question
Read and Follow Instructions Carefully: Show all your work by steps for each problem, beginning with stating the null hypothesis, and then show the appropriate formula, then show that formula with all values substituted into the formula, and then show major intermediate calculation steps as appropriate. Indicate the result of the statistical test and hypothesis decision you make, followed by a short written statement of your conclusion that derives from your hypothesis testing decision. Neatness counts! Darin’s who cannot read what your writing, cannot give you credit.
PROBLEM 1
Analyze data from simple study to compare Cognitive Behavior Therapy (CBT) and the drug Zoloft for treating Post Traumatic Stress Disorder. The data are shown below.
Conduct an ANOVA followed by multiple comparisons using LSD tests and effect size estimates using both d and r effect size calculation that compare each method to each other. Scores for each subject represent subject performance on an assessment of symptoms after 8 weeks of treatment or no treatment. Higher scores indicate more symptoms.
No Treatment Scores CBT Scores Zoloft Scores
27 22 20
21 19 26
25 21 15
26 20 13
25 23 17
Explanation / Answer
No Treatment Scores
CBT Scores
Zoloft Scores
27
22
20
21
19
26
25
21
15
26
20
13
25
23
17
X1
X2
X3
24.8
21
18.2
X
21.33333333
SSA=5(24.8-(21.33))^2……5(18.2-(21.33))^2=109.73
SSW=(27-(24.8))^2….(17-(18.2))^2=133.6
MSA=109.73/(3-1)=54.87
MSW=133.6/(15-3)=11.13
F=54.87/11.13=4.93
F crit=3.89
F>FCRIT, hence reject the null hypothesis
Anova: Single Factor
SUMMARY
Groups
Count
Sum
Average
Variance
No Treatment Scores
5
124
24.8
5.2
CBT Scores
5
105
21
2.5
Zoloft Scores
5
91
18.2
25.7
ANOVA
Source of Variation
SS
df
MS
F
P-value
F crit
Between Groups
109.73
2
54.87
4.93
0.03
3.89
Within Groups
133.60
12
11.13
Total
243.33
14
DF c=3 and (n-c)=(15-3)=12, Qa=3.77
Tukey Kramer Test: -
CR=Qa* MSW/2(1/n+1/n)
CR= 3.77*11.13/2*(1/5+1/5)
= 3.77*1.49
= 5.62
Means
Values
X1-X2
3.8
X1-X3
6.6
X2-X3
2.8
Only X1-X3 is greater than 5.62 and hence there is difference between X1 and X3.
Effect Size: -
n^2=SSbetween/SStotal=109.73/243.33=0.45
No Treatment Scores
CBT Scores
Zoloft Scores
27
22
20
21
19
26
25
21
15
26
20
13
25
23
17
X1
X2
X3
24.8
21
18.2
X
21.33333333
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